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Geometric Progression of Powers of Three

Source: 2014 AMC 12A #7

February 5, 2014
ratiogeometric sequenceAMC

Problem Statement

The first three terms of a geometric progression are 3\sqrt 3, 33\sqrt[3]3, and 36\sqrt[6]3. What is the fourth term?
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>37<spanclass=′latex−bold′>(C)</span>38<spanclass=′latex−bold′>(D)</span>39<spanclass=′latex−bold′>(E)</span>310<span class='latex-bold'>(A) </span>1\qquad <span class='latex-bold'>(B) </span>\sqrt[7]3\qquad <span class='latex-bold'>(C) </span>\sqrt[8]3\qquad <span class='latex-bold'>(D) </span>\sqrt[9]3\qquad <span class='latex-bold'>(E) </span>\sqrt[10]3\qquad
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